where \(\mbox{\textit {Nu}}_e\)  is the heat transfer estimated from the GL theory [1]}, [2]} for the equivalent single-phase system with \(\mbox{\textit {Ra}}^*=2\bar{\theta }\mbox{\textit {Ra}}\) , \(\theta _{hot}=2\bar{\theta }\)  and \(\theta _{cold}=0\) . In the two-phase system and the equivalent single-phase system, the dimensional heat transfer \(Q\)  (\(=\mbox{\textit {Nu}}\,k(\theta _{hot}-\theta _{cold})/H\) ) should be the same, which yields
\(\mbox{\textit {Nu}}(\mbox{\textit {Ra}},\mbox{\textit {Pr}},S_0,\tilde{h},n)=2\bar{\theta } \mbox{\textit {Nu}}_e(\mbox{\textit {Ra}}^*,\mbox{\textit {Pr}}),\) 
